/**
 * @author tmh
 * @date 2024/10/24 16:45
 * @description
 */
public class T64最小路径和 {

    public int minPathSum(int[][] grid) {
        int m = grid.length;
        int n = grid[0].length;
        int[][] dp = new int[m][n];
        //dp[i][j]表示到grid[i][j]的路径最小值
        dp[0][0] = grid[0][0];
        //第一行
        for (int i = 1; i < n; i++) {
            dp[0][i] = dp[0][i - 1] + grid[0][i];
        }
        //第一列
        for (int i = 1; i < m; i++) {
            dp[i][0] = dp[i - 1][0] + grid[i][0];
        }
        //其他格子
        for (int i = 1; i < m; i++) {
            for (int j = 1; j < n; j++) {
                dp[i][j]=Math.min(dp[i-1][j],dp[i][j-1])+grid[i][j];
            }
        }
        return dp[m-1][n-1];
    }
}
